砂堆雪崩幂律分布现象的解释

Another Explanation of Sand Pile Avalanches Power Law Distribution

自组织临界性的提出者Per Bak认为,处于临界状态砂堆雪崩呈现幂律分布,可作为广延耗散动力系统自组织临界性存在的证据。采用真实砂堆试验和元胞自动机砂堆模拟两种方法进行研究,提出处于亚临界状态的砂堆,在向临界状态演化的过程中,砂堆在亚临界状态发生众多小规模的雪崩,越接近临界状态,系统的波动越强,大规模的雪崩也时而发生,因此在从亚临界状态向临界状态演化的过程之中,大规模雪崩的发生次数少,小规模雪崩发生的次数多,雪崩发生的规模也呈现幂律分布,并认为这种情况更具普适性。

Per Bak, the introducer of Self-organized Criticality, thought that power-law distribution was the evidence for Self-organized Criticality, and the non-characteristic scale phenomenon which was presented in extended dissipative power systems in the self-organized critical state. Per Bak＇ s theoretical evidence was the sand pile model in the self-organized critical state. So the real sand pile experiment and sand pile experiment simulated by computer have been carried out in our research. It can be put forward that many small-scale avalanches take place in the subcritical state in sand pile, and the closer to the critical state, the stronger the system fluctuates, then large-scale avalanches emerge now and then. So the occurrence of the large-scale avalanches is less often than the small-scale avalanches when sub-critical state approaches to the critical state. The scale of avalanches presents power-law distribution. This kind of situation is regarded to be more universal than former theories from Per Bak.